Question: Simplify the following expression: $z = \dfrac{32x + 72}{72x + 16}$ You can assume $x \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $32x + 72 = (2\cdot2\cdot2\cdot2\cdot2 \cdot x) + (2\cdot2\cdot2\cdot3\cdot3)$ The denominator can be factored: $72x + 16 = (2\cdot2\cdot2\cdot3\cdot3 \cdot x) + (2\cdot2\cdot2\cdot2)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $z = \dfrac{(8)(4x + 9)}{(8)(9x + 2)}$ Dividing both the numerator and denominator by $8$ gives: $z = \dfrac{4x + 9}{9x + 2}$